|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||An inhomogeneous elliptic complex||Journal:||Journal d'Analyse Mathématique||Volume:||61||Issue:||1||First page:||367||Last page:||393||Issue Date:||1-Jan-1993||Rank:||M22||ISSN:||0021-7670||DOI:||10.1007/BF02788849||Abstract:||
We define a 3 term sequence P of differential operators of mixed type; the first and third operators are 1st order while the second operator is 2nd order. P is always elliptic; it forms a complex if M is einstein. It was first discussed by Gasqui. P is related to similar complexes C and G discussed by 02 Calabi and Gasqui-Goldschmidt. The index and equivariant index of P vanish. In dimension 2, P=C⊗s where S is of Dirac type;C and-S determine the same equivariant index. We study the heat equation asymptotics of the operators of P; the associated Laplacians do not have scalar leading symbol.
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